Well, so, for some reason, I got it in my head that it would be easy to win a 10-planet snake map with a Champion.
I was additionally compelled to activate and pursue the Fallen Spire campaign, to select SSB as my starting special ship (incidentally ceding Medic Frigates and Tackle Drone Launchers to the AI) and upgrade it to the max (thereby squandering my starting knowledge), leave CSG on, as well as Marauders and Spire Civilian Leaders.
And, for some reason, also crank the difficulty up to 8 (luckily I had enough sense to set them to vanilla).
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HELP!!!
Wow, you did indeed ramp up the difficulty here.
10-planet maps are quite difficult at any time. You have so little Knowledge to acquire for upgrades, and very little potential for manuever.
This is doubly compounded by the Fallen Spire campaign. The full campaign requires more planets than even exist in a 10-planet galaxy. This means you started the campaign, invoked the hard stuff, but were unable to go far enough to get to the final payoff.
In addition, you chose the Snake map-type. This map is very difficult, as you've discovered, because one of the homeworlds usually sits between you and some CSGs. While it does provide an easy choke-point for defense, it also means the AI has chokepoints against your expansion.
Minor factions provide some extra fun to the game, but I would recommend not using any until you're more familiar with the base game. Fallen Spire, for example, results in an ENTIRELY different style of play than the normal game.
Difficulty 7 is where the 'real game' begins, as it has been said. That's where the AI stops being tied down or restricted in its behaviors. At all difficulties above 7, the AI starts getting bonuses. So, 6 or 7 is probably where you want play your next few games. Once you are winning regularly on 7, you can move up and start losing again.
Don't be concerned about losing. Unlike Starcraft or more main-stream RTSs, AI War is a game you WILL lose regularly if you are playing at your skill level. I lose at least once in probably 2/3rds of the games I start. I just keep good saves, so I can go back and try again with a 'lessons learned'.
I downloaded your game and take a look.
First impression: Ouch.
Your AIP is almost 250 - This is very high, even for late-campaign Fallen Spire. As I'm sure you noticed, when the AIP goes up, the AI gets nastier. Waves get larger, reinforcements get bigger, and the AI's units get tougher. Try to keep the AIP as low as possible.
Related to this - Warheads. You've used a bunch of warhead, I think. This drives the AIP up quickly. While useful for "OMG, I'm gunna die!" moments, try to avoid using them at all elsewhere.
Also related to AIP - Every planet you take is at least 20 AIP (5 for the warp gate, 15 for the Command Station). Try to take as few planets as you must. You chose Snake map, 10-planet, Fallen Spire, so you didn't have all the much choice in the matter, but this a general principle to keep in mind.
The AI Homeworld you are next to is so nasty, in part, because you captured the Core World next to it. This put the Homeworld into an 'Alerted' state. When alerted, the AI gets more, and more frequent, reinforcements. Try to avoid alerting Core Worlds and Homeworlds, as this will help prevent those 3,000 ship swarms of AI ships.
Knowledge. Knowledge is always limited. 3,000 per planet. Thus, the larger the galaxy, the more Knowledge exists. But each planet either needs to be captured (at a 20 AIP cost) or hacked. It looks like you K-raided the AI Homeworld? Brave, but if you had enough control of the system to do that, why did you lose control?
What you spent your K on in this game was a little hasty. SSBs are nice ships, dangerous raiders and good at handling several times their number in fleetships. But unlocking Mk III takes 8,500K. That's a LOT - about 3 planets worth. Consider how useful your SSBs were to you. As raiders, SSBs are great. As ships-of-the-line in huge fleet battles, where the Cloaking isn't useful, they lose some of their advantages.
You also unlocked Plasma Siege and Bomber Starships Mk III. Since you had a ASC, this gave you the Mk IVs as well. And while those are powerful ships, are they worth 8,000K in your fleet? Those starships also cost a lot of resources to build.
You did not unlock any additional turrets or Fortresses.
You did not unlock any additional Force Fields.
You did not unlock ANY economic enhancers, either.
The lack of economy upgrades may have been the largest impact in your game. Frequently, dealing with the AI's powerhouse locations (such as Homeworlds) require several suicide attacks. By wearing down the AI's ship count a bit at a time, you can eventually get to the level where you have the advantage. However, the AI rebuilds, too, with time. Altenately, when defending against the AI, rebuilding your turrets and fleetships is criticla to preventing the AI from wearing YOU down.
So being able to quickly rebuild is important. By upgrading you would be able to rebuild 2-3 times faster. This is very important, and can easily spell the difference between recovering from losses and getting into a death-spiral.
Unlocking additional turrets not only improves your defenses, allowing you to survive larger AI attacks, it also improves several things offensively. For example, unlocking Needler Mk II, you also get access to Drones produced by the Neinzul Enclave ships. Unlocking turrets is also one way to enhance your Modular Fortresses. Finally, unlocking certain turrets allows you to enhance your Fallen Spire vessels.
Forcefields also apply to Fallen Spire ships. But mostly, they're there to keep the AI from killing you! Your precious Advanced Factories, Starship Constructors, or Fabricators need something to protect them. Higher mark forcefields are significantly more powerful, and just as importantly, there are simply more of them available.
The Champion's experience works like Knowledge. There's a limited amount, and you can't un-spend it. You unlocked level 2 of a great many types of modules, but you end up not using most of them. This means you're unable to access the high-level Mk IV and V modules that are so very powerful and can greatly increase the strength of your Champion.
Your current in-game situation is pretty hopeless. The AI has more than enough ships to steamroll you, but at the moment it hasn't.
You did well grinding down the Gravity Reactors, allowing you through the system. Transports and Cloakers can help you get your fleet past the homeworld. But to do that, you need to enhance your fixed defenses. Currently, if you remove your fleet, the AI ships in the Homeworld can easily overwhelm your system. By building more defenses, you might be able to hold them back better. Build more turrets, especially Grav turrets near the wormhole. You can try 'baiting' the AI into attacking your systems by moving your mobile fleet back a system or two, then returning when the attack starts. You'd need to expect major losses if that happens. The fact that you have a ZPG in that system is unfortunate, as you'll probably lose it if any attack occurs.
As an alternative, you could just use your Champion and Starships to make suicide runs against the AI homeworld and wear down the fleet a little, until you can use Transports to move the rest of your fleet past the Homeworld. Once in a system with the CSG-A, dump your holds, ignore everything else to take out the AI Command Station, build your own Station (A seperate transport loaded with a Colony Ship and a bunch of Engineers is useful here), and kill the CSG. After that, run away. Don't try to protect those fabs, you can't. But with all the CSGs down, you'll be able to perform suicide runs against the AI Homeworld's guardposts.
Either approach is looking at a LOT of grind, however. I played an hour or so at +10 speed, and only killed about 10% of the AI's hordes. I'd expect at least another 8 hours, possibly more. And all that time, a mistake or bad luck (or the RNG going against you) will give the AI the push it needs to overrun you.
As it stands, removing 50% of your fleet from the front lines is enough to get the AI to attack - but without major reduction in its fleet, it WILL kill you.
All in all, I'd suggest taking some lessons from this experience, and start again with a new game.